There are composers, like artists, that changed the way you perceive music. Usually they began before a movement or during it.
When movements occur, they affect all the arts and literature. They affect each other. There is something about ideas that shape their arts.
Example: Impressionism. You have your impressionist painters like Monet, Degas, Pissarro, Renoir, Etc. Then you have the impressionist musicians---composers, like Debussy and Ravel. In literature they were called Symbolists: Baudelair, Mallarme, Rimbaud, Verlaine, and Laforgue.
